The balance between the exploration and the exploitation plays a significant role in the meta-heuristic algorithms, especially when they are used to solve large-scale optimization problems. In this paper, we propose a multiple-strategy learning particle swarm optimization algorithm, called MSL-PSO, to solve problems with large-scale variables, in which different learning strategies are utilized in different stages. At the first stage, each individual tries to probe some positions by learning from the demonstrators who have better performance on the fitness value and the mean position of the population. All the best probed positions, each of which has the best fitness among all positions probed by its corresponding individual, will compose a new temporary population. The temporary population will be sorted on the fitness values in a descending order, and will be used for each individual to find its demonstrators, which is based on the rank of the best probed solution in the temporary population and the rank of the individual in the current population, to learn using a new strategy in the second stage. The first stage is used to improve the exploration capability, and the second one is expected to balance the convergence and diversity of the population. To verify the effectiveness of MSL-PSO for solving large-scale optimization problems, some empirical experiments are conducted, which include CEC2008 problems with 100, 500, and 1000 dimensions, and CEC2010 problems with 1000 dimensions. Experimental results show that our proposed MSL-PSO is competitive or has a better performance compared with ten state-of-the-art algorithms.

探索与开发之间的平衡在元启发式算法中起着重要作用，尤其是当它们用于解决大规模优化问题时。在本文中，我们提出了一种多策略学习粒子群优化算法MSL-PSO，以解决大规模变量问题，其中在不同阶段采用了不同的学习策略。在第一阶段，每个人都试图通过向示威者学习来探究一些位置，这些示威者在适应性值和人口平均位置方面的表现更好。所有最好的探测位置（每个位置在其对应的个人探测的所有位置中具有最佳适应性）将组成一个新的临时人口。临时总体将按照适合度值从高到低的顺序排序，并将用于每个个体以找到其示威者，这是基于临时总体中最佳探测解决方案的排名和个体在最佳总体中的排名而定的。当前人群，以便在第二阶段学习使用新策略。第一个阶段用于提高勘探能力，第二个阶段有望平衡人口的收敛性和多样性。为了验证MSL-PSO解决大规模优化问题的有效性，进行了一些经验实验，包括100、500和1000维的CEC2008问题以及1000维的CEC2010问题。